Question: Solve for $x$ and $y$ using elimination. ${-3x+5y = 25}$ ${3x+2y = 31}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $7y = 56$ $\dfrac{7y}{{7}} = \dfrac{56}{{7}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x+5y = 25}\thinspace$ to find $x$ ${-3x + 5}{(8)}{= 25}$ $-3x+40 = 25$ $-3x+40{-40} = 25{-40}$ $-3x = -15$ $\dfrac{-3x}{{-3}} = \dfrac{-15}{{-3}}$ ${x = 5}$ You can also plug ${y = 8}$ into $\thinspace {3x+2y = 31}\thinspace$ and get the same answer for $x$ : ${3x + 2}{(8)}{= 31}$ ${x = 5}$